When the DaVinci Code first came out, there were all kinds of discussions in the popular press about whether Brown's fictional Professor Langdon really could hold a professorial chair in symbology at Harvard. General consensus was no:
Harvard: No Symbology Here
Can You Really Be a Professor of Symbology?
Apparently this is one more instance of the popular press misunderstanding the lengths to which we academics sometimes go to make sure we are very precise in our distinctions between terms and fields of study. To wit, while reading Michael Camille's Image on the Edge, I came across a reference to the following article:
Turner, Victor. "Liminal to Liminoid in Play, Flow and Ritual: An Essay in Comparative Symbology." Rice University Studies 60:3 (1974). 53-92.
Turner is (was?), the biographical information in the article explains, a professor of social thought and anthropology at the University of Chicago. So in keeping with the need to be very precise about this sort of thing, no, one cannot be a professor of Symbology. But that certainly shouldn't stop anyone from writing about it.